The solution of the given differential equation dy dx + 2xy = y i… - Vidyadip

MCQ

The solution of the given differential equation $\frac{{dy}}{{dx}} + 2xy = y$ is

✓
$y = c{e^{x - {x^2}}}$
B
$y = c{e^{{x^2} - x}}$
C
$y = c{e^x}$
D
$y = c{e^{ - {x^2}}}$

✓

Answer

Correct option: A.

$y = c{e^{x - {x^2}}}$

a
(a) $\frac{{dy}}{{dx}} + (2x - 1)y = 0$; $I.F.$ $ = {e^{\int_{}^{} {(2x - 1)dx} }} = {e^{{x^2} - x}}$

Required solution is $y{e^{{x^2} - x}} = c$or$y = c{e^{x - {x^2}}}$.

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